What is the total impedance ZT of a series network consisting of a 5 Ω resistor, an inductor having 10 Ω reactance, and a capacitor with 15 Ω reactance?
Question
What is the total impedance Z<sub>T</sub> of a series network consisting of a 5 Ω resistor, an inductor having 10 Ω reactance, and a capacitor with 15 Ω reactance?
Solution
The total impedance (ZT) of a series network consisting of a resistor (R), an inductor (L), and a capacitor (C) can be calculated using the formula:
ZT = sqrt[(R^2) + (XL - XC)^2]
where:
- R is the resistance,
- XL is the reactance of the inductor, and
- XC is the reactance of the capacitor.
Given that R = 5 Ω, XL = 10 Ω, and XC = 15 Ω, we can substitute these values into the formula:
ZT = sqrt[(5^2) + (10 - 15)^2] = sqrt[(25) + (-5)^2] = sqrt[(25) + (25)] = sqrt[50]
Therefore, the total impedance ZT of the series network is sqrt[50] or approximately 7.07 Ω.
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